1. Field of the Invention
The present invention relates to a processing technique for Kalman Filter. More particularly, the present invention relates to a technique of making improvement on an estimation error in the Kalman Filter.
2. Description of Related Art
A nonlinear state space model has been conventionally used as a model for designing a controller of a plant for an engine, control of the attitude of a satellite, a lithium ion battery, a fuel cell, and etc. The nonlinear state space model is complex as a whole, but it includes subsystems, where the subsystems' physical and chemical laws are known to some extent.
One generally estimates the internal states of the nonlinear state space model by linearly approximating a nonlinear function. Such method of linearly approximating a nonlinear function has employed a configuration based on Extended Kalman Filter (EKF).
However, the increase of model-based development lead to an increase of physical and chemical descriptions of a plant. As a result, there has been an increase of demand for development of a controller without unnecessary operation. In these circumstances, new challenges are presented, such as: providing a general framework of nonlinear system identification and state estimation that avoids a linear approximation and reflect properties of the plant in more detail; and providing a technique of designing a control system having high performance, which takes advantage of enhanced accuracy of the nonlinear system identification and state estimation.
To address such challenges, Unscented Kalman Filter (UKF) is proposed as a framework capable of handling a nonlinear function without approximation for a discrete system for which a Jacobian matrix or Hessian matrix cannot be calculated. UKF can also handle a wider error range of the first order approximation. It is known that the UKF can estimate better than the EKF can.
Further, it is known that augmented UKF has better accuracy than general filtering based on the state space model.
A conventional augmented UKF directly uses a nonlinear function representing plant characteristics and allows macro characteristics to be known, where the relative levels of frequency components can be known. However, the augmented UKF is based on the assumption that sampling for a filter update is performed at uniform timing. These conventional techniques do not consider that a temporal or frequency resolution can partly vary due to the nonlinear function.